The battery is fully charged and when I turn the key on, I don't get the green light. When I pull start it, it starts up on the first pull, then everything works. Maybe there is a short somewhere.

 

My uncle and cousin(s) both have 1998 Honda Foreman ES. They live really close nearby so ill ride them every now and then. But anyway they both have had this problem. I always had to pull start it, even after we recharged the battery. I think what you have to do is when you are riding it, ride it for a good while, LONG and HARD. I dont mean tear your quad up or anything but try and rev it up a good bit, and get the battery pumpin. I love Foreman 450's, ESpecially the ES. See if this helps. After reving it up and driving for about 30 minutes, ill get off, let it chill for about 30 more minutes and then go back out, and usually it'll crank right back up and be ok. But it may take more than 1 time. Keep on charging it though, it can only help.
----------------------------
2004 Polaris Sportsman 700 (Green)
'27 ITP 589 M/S Tires
on ITP Type 5 Wheels
3000 lb. Warn Winch
3-Way Headlight Mod
High Lifter Lift Kit

2004 Polaris Sportsman 500 Mossy Oak - STOLEN
2001 Honda Rancher ES 350
Winch
Sold

 

Im thinking it just the opposite, not a short but a very high resistance connection.
Hows the connections at the battery? Oxidized? tight?
You could also check the connection at the gear position sensor, and make sure its clean, non oxidized and snug.

 

If the meter and other lights come on, its probably not your battery. Like hondabuster said, check the nuetral lite circuit. Disconnect the gear position sensor connector and check for continuity thru to the nuetral switch. You can then jump the nuetral lite wire from the harness side connector to ground. If the lite comes on, your problem is from the connector to the switch. If it doesn't come on, the problem is from the connector up thru the harness somewhere.

 

Check all your fuses, especially the main battery fuse in a seperate holder from the main fuse block, its well marked behind the battery. The bike WILL run with the main fuse gone, on pull start as you describe.